In the TeV energy region and above, the uncertainty in the level of prompt
atmospheric neutrinos would limit the search for diffuse astrophysical
neutrinos. We suggest that neutrino telescopes may provide an empirical
determination of the flux of prompt atmospheric electron and muon neutrinos by
measuring the flux of prompt down-going muons. Our suggestion is based on the
consideration that prompt neutrino and prompt muon fluxes at sea level are
almost identical.Comment: 4 pages, 3 figure

A.D. Martin

E. Zas

E.V. Bugaev

G. Gelmini

Gabriele Varieschi

Graciela Gelmini

H.L. Lai

L. Pasquali

M. Aglietta

M. Nagano

M. Thunman

M.L. Mangano

O.G. Ryazhskaya

P. Lipari

Paolo Gondolo

R. Gandhi

T. Sjöstrand

T.K. Gaisser

T.S. Sinegovskaya

English

arXiv

Crossref

Measuring the prompt atmospheric neutrino flux with down-going muons in neutrino telescopes

In the TeV energy region and above, the uncertainty in the level of prompt atmospheric neutrinos would limit the search for diffuse astrophysical neutrinos. We suggest that neutrino telescopes may provide an empirical determination of the flux of prompt atmospheric electron and muon neutrinos by measuring the flux of prompt down-going muons. Our suggestion is based on the consideration that prompt neutrino and prompt muon fluxes at sea level are almost identical

Gelmini, Graciela

Gondolo, Paolo

Varieschi, Gabriele

Loyola Marymount University

Digital Commons@Loyola Marymount Universityand Loyola Law SchoolPhysics Faculty Works Seaver College of Science and Engineering1-1-2003Measuring the prompt atmospheric neutrino fluxwith down-going muons in neutrino telescopesGraciela GelminiUniversity of California, Los AngelesPaolo GondoloCase Western Reserve UniversityGabriele Varieschigvarieschi@lmu.eduThis Article - post-print is brought to you for free and open access by the Seaver College of Science and Engineering at Digital Commons @ LoyolaMarymount University and Loyola Law School. It has been accepted for inclusion in Physics Faculty Works by an authorized administrator of DigitalCommons@Loyola Marymount University and Loyola Law School. For more information, please contact digitalcommons@lmu.edu.Repository CitationGelmini, Graciela; Gondolo, Paolo; and Varieschi, Gabriele, "Measuring the prompt atmospheric neutrino flux with down-goingmuons in neutrino telescopes" (2003). Physics Faculty Works. 48.http://digitalcommons.lmu.edu/phys_fac/48Recommended CitationGelmini, G., P. Gondolo, and G. Varieschi, Phys. Rev. D 67, 017301 (2003). https://doi.org/10.1103/PhysRevD.67.017301arXiv:hep-ph/0209111v1  10 Sep 2002UCLA/02/TEP/23, CWRU-P13-02, NSF-ITP-02-97Measuring the prompt atmospheric neutrino flux with down-going muons in neutrinotelescopesGraciela Gelmini1, Paolo Gondolo2, and Gabriele Varieschi31Department of Physics and Astronomy, UCLA, Los Angeles, CA 90095-15472Department of Physics, Case Western Reserve University, 10900 Euclid Ave., Cleveland OH 44106, USA3Department of Physics, Loyola Marymount University, One LMU Drive, Los Angeles CA 90045, USA(September, 2002)In the TeV energy region and above, the uncertainty in the level of prompt atmospheric neutrinoswould limit the search for diffuse astrophysical neutrinos. We suggest that neutrino telescopes mayprovide an empirical determination of the flux of prompt atmospheric electron and muon neutrinosby measuring the flux of prompt down-going muons. Our suggestion is based on the considerationthat prompt neutrino and prompt muon fluxes at sea level are almost identical.Atmospheric neutrinos and muons, i.e. neutrinos andmuons produced in the atmosphere by cosmic ray inter-actions, are the most important source of backgroundfor present and future high-energy neutrino telescopes,which are expected to open a new window in astronomyby detecting neutrinos from astrophysical sources [1]. (Inthis Letter, ‘muons’ includes ‘antimuons’ and ‘neutrinos’includes ‘antineutrinos’.)In their current design, neutrino telescopes consist oflarge arrays of phototubes located under water or ice.They detect high-energy neutrinos through the chargedparticles these produce in the water or ice inside oraround the instrumented array.Atmospheric muons can reach the detector only fromabove, because the range of muons in Earth is only a fewkilometers. Atmospheric muons are therefore only down-going. Their flux is typically so high that the region ofsky accessible to even very deep neutrino telescopes isonly the hemisphere below the horizon.Atmospheric neutrinos can instead reach the detectorfrom all directions. Hence they are an irreducible back-ground for diffuse astrophysical neutrino fluxes. It istherefore very important to evaluate their intensity withreasonable accuracy.At GeV energies the atmospheric muon and neutrinofluxes are dominated by ‘conventional’ sources, i.e. de-cays of relatively long-lived particles such π and Kmesons. With increasing energy, the probability in-creases that such particles interact in the atmosphere be-fore decaying. This implies that even a small fraction ofshort-lived particles can give the dominant contributionto high energy muon and neutrino fluxes. These ‘prompt’muons and neutrinos arise through semi-leptonic decaysof hadrons containing heavy quarks, most notably charm.Estimates of the magnitude of the prompt atmosphericfluxes differ by almost 2 orders of magnitude. Fig. 1shows a compilation of prompt muon fluxes at sea level.Prompt neutrino fluxes are essentially identical, whileFIG. 1. Vertical atmospheric muon (and neutrino) fluxes.Muon and neutrino conventional fluxes from [2] (below 106GeV) and [3] (above) (line marked conven. and dashed lines).Muon prompt fluxes from: two charm production models in[4] (ZHVa, ZHVe); empirical model in [5] (RVS); quark-gluonstring model and recombination quark-parton model in [6](QGSM, RQPM); perturbative QCD in [7] (PRS band), [8,9](GGV band), and [3] (TIG). Also indicated are the experi-mental bounds on prompt muons from LVD [10] and AKENO[11].conventional neutrino fluxes are lower by one (νµ) or two(νe) orders of magnitude. The crossing from conventionalto prompt muon fluxes happens between 40 TeV and3 PeV, while the analogous crossing for muon-neutrinoshappens at lower energies, between 20 TeV and 800 TeV.1The uncertainty in the intensity of conventional atmo-spheric neutrinos and muons is thought to be approxi-mately 30% at present, but could decrease to about 10%with coming improvements [12]. At about 1 TeV, thecontribution of prompt neutrinos taking into account theLVD bound could be as high as 10% of the conventionalneutrino flux.Between 1 TeV and 100 TeV, prompt neutrinos be-come the biggest source of uncertainty in the atmosphericneutrino flux. So the level of prompt neutrinos is a po-tential problem which would limit the search for diffuseastrophysical neutrinos at energies of about 1 TeV, muchsmaller than the energies where they become dominant(see for example [12]).Here we suggest a way to overcome the theoretical un-certainty in the magnitude of the prompt electron andmuon neutrino fluxes by deriving their intensity from ameasurement of the down-going prompt muon flux. Oursuggestion is based on the observation that, due to thecharmed particle decay kinematics and the same branch-ing ratios for the semi-leptonic decays into eνe and µνµ,the prompt electron and muon neutrino fluxes and theprompt muon flux are essentially the same at sea level[3,7–9,13]. This result is independent of the charm pro-duction model.We want to stress that we are suggesting to use down-going prompt muons and not up-going neutrino-inducedmuons whose flux is orders of magnitude smaller. Whilean important contribution to up-going muons is expectedfrom astrophysical neutrinos, no astrophysical signal isexpected in down-going atmospheric muons.Moreover, prompt muons are much easier to detectthan prompt neutrinos, since the latter have to convertto a charged particle within the effective volume of thedetector. In fact, the flux of upcoming muons induced bymuon neutrinos at 1 TeV is about 10−7 of the neutrinoflux at sea level (using charge-current cross sections in[14] and muon ranges in [15]). On the other hand, theflux of down-going muons at a slant depth of about 3 kmw.e. is only a fraction 0.4–0.6 of the muon flux at sealevel (the exact suppression factor depending on depth,energy spectra and zenith angle [15]). Thus close to 1TeV, taking into account that the conventional neutrinofluxes at sea level are about 10% of the muon fluxes (seeFig. 4 below), for each up-going neutrino-induced muonthere are 4–6 107 down-going muons. Of these, as muchas a few percent may be prompt.From Fig. 1, the vertical conventional muon flux above1 TeV is approximately 1010 muons/km2/yr/sr at sealevel. This implies roughly 109 down-going events peryear in a kilometer-size detector at a depth of about 3km. Thus, to extract a 1% fraction of prompt muons at1 TeV, it would suffice to record 1 out of 105 down-goingevents per bin in the sky for a year (fewer events wouldneed to be recorded at higher energies).For what we suggest, it is important to separate theprompt muons from the conventional ones for two rea-sons: (1) the conventional neutrino fluxes are small frac-tions, less than 10%, of the conventional muon flux, andour method of using the ratio of neutrino to muon fluxeswould become less straightforward; and (2), as a con-sequence of the previous reason, the ratio of neutrino tomuon fluxes depends on the crossing energy between con-ventional and prompt fluxes, and so on the large uncer-tainty on the absolute value of the prompt fluxes, makingour method inapplicable.There are ways of separating the prompt muons fromthe conventional ones in underwater or under-ice detec-tors, such as the different zenith angle dependence of theprompt and conventional fluxes; the different depth de-pendence at a given zenith angle; and the different spec-tral shape at a given depth and zenith angle (see e.g.Ref. [16,17])In a series of papers [8,9,13] (called GGV1, GGV2and GGV3 from now on), we studied the prompt lep-ton fluxes using a model for charm production in the at-mosphere based on Quantum Chromo-Dynamics (QCD),the theoretically preferred model. We used a next-to-leading order perturbative QCD (NLO pQCD) cal-culation of charm production, as implemented in theMangano-Nason-Ridolfi program [18] calibrated at lowenergies, followed by a full simulation of particle cascadesin the atmosphere generated with PYTHIA routines [19].In our first paper (GGV1), we tried different modes ofcascade generation, different options allowed by PYTHIAin the various stages of parton showering, hadronization,interactions and decays, etc., noticing changes of at most10% in the final results. We decided to use what wecalled our ‘single’ mode simulation, with showering, in-dependent fragmentation, interactions and semileptonicdecays according to Ref. [3]. In our ‘single’ mode weenter only one c quark in the particle list of PYTHIA,and we multiply the result by a factor of 2 to accountfor the initial c̄ quark. PYTHIA performs the shower-ing, standard independent fragmentation, and follows allthe interactions and decays using default parameters andoptions.In GGV1 we found that the NLO pQCD approach pro-duces fluxes in the bulk of older predictions (not basedon pQCD) as well as of a pQCD semianalytical analysis[7]. We also explained the reason of the low fluxes of themodel of Ref. [3], which were due to the chosen extrapo-lation of the gluon partonic distribution function (PDF)at small momentum fractions x.In GGV2, we considered four sets of PDF’s: MRS R1-R2 [20], CTEQ 4M [21] and MRST [22]. Besides thechoice of the PDF set, our procedure has the freedomto choose reasonable values of the charm mass mc, thefactorization scale µF , and the renormalization scale µR,so as to fit the experimental data. In GGV1 and GGV2we made the standard choice [18,23] of µF = 2mT , µR =mT , where mT =√p2T + m2c is the transverse mass. The2FIG. 2. Ratio of prompt neutrino to prompt muon fluxesas a function of lepton energy using the MRST PDFwith λ = 0 (solid line), 0.1 (dotted), 0.2 (short-dashed),0.3 (long-dashed), 0.4 (short-dashed dotted), and 0.5(long-dashed dotted).values of the charm mass were taken slightly differentfor each PDF set, namely: mc = 1.185 GeV for MRSR1, mc = 1.310 GeV for MRS R2, mc = 1.270 GeV forCTEQ 4M, and mc = 1.250 GeV for MRST.Due to the steep decrease with increasing energy ofthe incoming flux of cosmic rays, only the most ener-getic charm quarks produced count and those come fromthe interaction of projectile partons carrying a large frac-tion of the incoming nucleon momentum. Thus, thecharacteristic x of the projectile parton, x1, is large,x1 ≃ O(10−1). We can then immediately understandthat very small parton momentum fractions are involvedin pQCD charm production as follows. Typical partoniccenter of mass energies√ŝ are close to the cc̄ threshold2mc ≃ 2 GeV, (since the differential cc̄ production crosssection decreases with increasing ŝ) while the total centerof mass energy squared is s = 2mNE (with mN ≃ 1 GeVthe nucleon mass, and E the energy per nucleon of the in-coming cosmic ray). Calling x2 the momentum fractionof the target parton in the nucleus of the atmosphere,we have x1x2 = ŝ/s = 4m2c/(2mNE) ≃ GeV/E. Hencex2 ≃ O(GeV/0.1 E) ≃ O(GeV/El), where El ≃ 0.1E isthe dominant muon or neutrino energy.In GGV2, we analyzed in detail the dependence of thefluxes on the extrapolation of the gluon PDF at small x,which, according to theoretical models, is assumed to bea power law with exponent λ, xg(x) ∼ x−λ, with λ in therange 0–0.5. Particle physics experiments are yet unableto determine the value of λ at x < 10−5. We found thatFIG. 3. As Fig. 2, but for CTEQ 4M and λ = 0 and 0.5.the choice of different values of λ at x < 10−5 leads to awide range of final prompt fluxes at energies above 105GeV.Due to this result, in GGV2 and GGV3 we suggestedthe possibility of measuring λ through the atmosphericmuon fluxes at energies above 105 GeV, using not the ab-solute fluxes, because of their large theoretical error, butrather their spectral index (i.e. the “slope” of the flux).In particular, in GGV3 we proposed to use the slope ofthe flux of down-going prompt muons, and presented anoverall error analysis of the model we used.Here again we are suggesting to use down-goingprompt muons, at energies Eµ >∼ 1 TeV where promptmuons can be separated from conventional ones [17], thistime to measure the flux of prompt electron and muonatmospheric neutrinos at sea level. We find that the ratioof prompt neutrino to prompt muon fluxes is about 1.1,constant with energy to within 10%, and almost indepen-dent of the choice of PDF and charm production param-eters. This is shown in Figs. 2 and 3 for the MRST andCTEQ 4M PDF’s with a range of λ values from 0 to 0.5.We do not show results obtained with the MRS R1 andR2 PDF’s because they are similar. We expect that othermodels of charm production in the atmosphere, even notbased on perturbative QCD, will lead to a similar ratio,because this ratio depends essentially only on the decayproperties of the charmed hadrons.To complete the discussion, in Fig. 4 we plot theneutrino-over-muon ratio of the sum of conventional plusprompt lepton fluxes as a function of lepton energy. Inthis figure, we use the conventional fluxes in Ref. [3] andthe prompt fluxes of GGV2 with the MRST PDF and3FIG. 4. Total neutrino-over-muon ratio as a function oflepton energy. Vertical marks denote the crossing energy fromconventional to prompt muons.λ = 0 (thick lines) and 0.5 (thin lines). For each λ,the crossing energy from conventional to prompt muons,from Fig. 2 in GGV2, is marked with a vertical stroke.We have suggested a way to overcome a potential prob-lem which would limit the search for diffuse astrophysicalneutrinos in underwater or under-ice neutrino telescopes,namely the theoretical uncertainty of about two ordersof magnitude in the intensity of the prompt atmosphericneutrino fluxes. Concretely, we have suggested to deter-mine their intensity from a measurement of the down-going prompt muon flux at sea level, whose intensity isthe same to within 10% or better.This work was supported in part by U.S. Departmentof Energy grant DE-FG03-91ER40662 TaskC at UCLA,and in part by National Science Foundation under GrantNo. PHY99-07949 at the Kavli Institute for TheoreticalPhysics at UCSB. G.V. was supported by an award fromResearch Corporation.[1] T. K. 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Gaisser, talk at NEUTRINO 2002, Munich, Germany,2002; T. K. Gaisser and M. Honda, Ann. Rev. Nucl. Part.Sci., to appear [hep-ph/0203272].[13] G. Gelmini, P. Gondolo, and G. Varieschi, Phys. Rev. D63, 036006 (2001).[14] R. Gandhi, C. Quigg, M. H. Reno and I. Sarcevic, Phys.Rev. D 58, 093009 (1998).[15] P. Lipari and T. Stanev, Phys. Rev. D 44 (1991) 3543.[16] E. V. Bugaev et al., Phys. Rev. D 58, 054001 (1998).[17] T. S. Sinegovskaya and S. I. Sinegovsky, Phys. Rev. D 63(2001) 096004.[18] M.L. Mangano, P. Nason, and G. Ridolfi, Nucl. Phys. B373, 295 (1992); Nucl. Phys. B 405, 507 (1993).[19] T. Sjöstrand, Comput. Phys. Commun. 82, 74 (1994).[20] A.D. Martin, R.G. Roberts and W.J. Stirling, Phys. Lett.387, 419 (1996).[21] H.L. Lai et al., Phys. Rev. D 55, 1280 (1997).[22] A.D. Martin, R.G. Roberts, W.J. Stirling, and R.S.Thorne, Eur. Phys. J. C 4, 463 (1998).[23] S. Frixione, M.L. Mangano, P. Nason, and G. Ridolfi,Report No. CERN-TH/97-16, hep-ph/9702287.4

Measuring the prompt atmospheric neutrino flux with down-going muons in
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Measuring the prompt atmospheric neutrino flux with down-going muons in neutrino telescopes

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